Week 3 Answer Key
Econ 210D
K.D. Hoover
Spring 2015
Corrected, 4 February 2015
Week 3 Answer Key
Problem 2.16: Using the post-World War II data and the rule of thumb, the recessions in the
U.S. economy are as follows:
1948:4-1949:2, 1953:2-1954:1, 1957:3-1958:1, 1969:3-1970:1, 1974:2-1975:1,
1980:1-1980:3, 1981:3-1982:1, 1990:3-1991:1, 2008:2-2009:2
There is a two quarter-fall at the very beginning of the data, but it is hard to date a recession,
since we do not know what occurred before that.
A case can be made for two alterations to this dating scheme (students might argue for others:
First, the trough of the first recession might be placed at 1949:4 instead of 1949:2. Here are
the changes in real GDP around that period:
1948:4
1949:1
1949:2
1949:3
1949:4
1950:1
+ 2.2
–27.8
– 6.7
+22.0
–18.1
+79.9
Although real GDP rises in 1949:3, the rise is smaller than the cumulated fall of the preceding
two quarters and is followed by a large fall, so that the net movement from 1948:4 to 1949:4
is a large and clear fall. It is only with the large rise in 1950:1 that unequivocal upward
growth resumes. I would thus, replace 1948:4-1949:2 with 1948:4-1949:4. A similar case
can be made to add a recession starting in 1960:1. The changes in real GDP around that date
are:
1960:1
1960:2
1960:3
1960:4
1961:1
+68.1
–11.9
+ 7.7
–37.8
+21.0
The brief uptick in 1960:3 is overwhelmed by the downticks in 1960:2 and 1960:4, leading
me to place a recession in 1960:1-1960:4. Thus the modified list of recessions is:
1948:4-1949:4, 1953:2-1954:1, 1957:3-1958:1, 1960:1-1960:4, 1969:3-1970:1, 1974:21975:1,1980:1-1980:3, 1981:3-1982:1, 1990:2-1991:1, 2008:2-2009:2
Problem 4.1:
20 1.00  20  0.75
100  140 .
20  0.75  20  0.50
30 1.00  18  0.75
P
P
 100 ; p2011
Paasche: p2010

100  138 .
30  0.75  18  0.50
L
L
 100 ; p2011
(a) Laspeyres: p2010

1
Week 3 Answer Key
Econ 210D
K.D. Hoover
Spring 2015
Corrected, 4 February 2015
F
 100 ; p2011
Fisher-ideal: p
 140 138  139.
(b) Chain-weighted index = Fisher-ideal index when there are only two years. Real GDP for
2010 = nominal GDP when 2010 is the base year. Thus, Y2010 = 20  0.75  20  0.50 = 25
100
and Y2011  (30 1.00  18  0.75)
 31.29 .
139
139
(c) Y2010  (20  0.75  20  0.50)
 34.75 . Real GDP for 2011 = nominal GDP when 2011
100
is the base year. Thus, Y2011 = 30 1.00  18  0.75 = 43.50 and
P
2010
Problem 4.6:
(a) The Laspeyres index for 2010 is 102.0.
(b) The CPI in 2010 in 1982-84 dollars should be 180.9  (102.0/100) = 184.5.
(c) The value of the CPI in 2002 with 1967 as the reference year 541.9  (102.0/100) = 552.7?
(d) Paasche index for 2010 = 102.1; the chain index = 102.0 [Note: the chain index and the
Laspeyres index do differ, but only in the second decimal place]. In the text we argued
that the Paasche index would be lower than the Laspeyres index. That is not true here.
The reason why can be seen from calculating the rates of inflation for individual goods.
Normally, we would expect demand to shift from the goods with the increasing relative
prices to those with decreasing relative prices. But that does not always happen – for
example if tastes change. Here, for example, food and beverages have the second fastest
rate of price increase, and their share falls as expected. However, medical care has the
fastest rate of price increase, yet its share rises rather than falls, most likely because
changing demographics – especially an older population – has shifted tastes toward more
medical care independent of the change in relative prices.
Problem 4.7: No answer provided as it is discussed in detail in the text.
Problem 4.8: The general method of conversion is $2011:11 pt  $t pt
CPI U
p2011
:11
. The price level in
ptCPI U
the target year is $2011:11 pt  227.1 .
Price Actual Year
CPI Actual Year
Price 2011:11
(November)
(i) Men’s Sport Coat 11/60
(ii) Coffee 11/65
(iii) Ford Galaxie 11/72
(iv) Reclining Chair 11/81
(v) Washing Machine 11/88
22.85
1.09
3,939.00
299.00
604.00
2
29.8
31.8
42.4
93.8
120.3
174.13
7.78
21,097.80
723.91
1,140.22
Week 3 Answer Key
Econ 210D
K.D. Hoover
Spring 2015
Corrected, 4 February 2015
ptGDP deflator
, where t = 1948:1 or
GDP deflator
p1998
:3
1980:4. Note the relevant price indices are 1948:1 = 13.4, 1980:4 = 46.0, and 1998:3 = 79.0.
p GDP:1deflator
13.4
 $1998:3169
 28.67 . Using
For example, for (i) in 1948:1: $1948:1 pt  $1998:3169 1948
GDP deflator
p1998:3
79.0
the same method:
Problem 4.9: The general rule for conversion is $t pt  $1998:3 pt
(i) Vacuum Cleaner
(ii) Cookware Set
(iii) Man’s Sportshirt
(iv) Television
(v) Personal Computer
Price 1998:3
169.00
299.99
24.99
219.99
604.00
3
Price 1948:1
28.67
50.88
4.24
37.31
102.45
Price 1980:4
98.40
174.68
14.55
128.09
351.70
Week 3 Answer Key
Econ 210D
K.D. Hoover
Spring 2015
Corrected, 4 February 2015
Problem 5.1:
Note that the recession period from the NBER below is defined as the period from the quarter
at the peak to the quarter at the trough (for example, if the peak is in January and the trough is
in July of the same year, the recession is from the first to the third quarter of that year). Table
5.1.1 compares the NBER recession dates with the dates from the two-quarter rule as in
Problem 2.16. (Note that these are the the pure rule-of-thumb dates and not those modified by
any other considerations.) Differences may occur because the NBER does not follow the
“rule of thumb” as we used in problem 2.16. Rather the NBER identifies recession using i)
depth as well as duration in the decline of the economic activity (note that, the rule of thumb
solely relies on the duration of the decline of real GDP) and ii) broader indicators than only
real GDP. Also the NBER uses monthly data while our calculation in problem 2.16 uses
quarterly. This can shift dates. For example, if recession starts in March (i.e. in the first
quarter), real GDP for the whole first quarter might not show a fall. Our rule of thumb would
put the peak a quarter later than the NBER.
Table 5.1.1: NBER Recessions and the Two-quarter Rule
The corresponding
Recession period from
recession period from
NBER
problem 2.16
1948:4-1949:4
1948:4-1949:2
1953:3-1954:2
1953:2-1954:1
1957:3-1958:2
1957:3-1958:1
1960:2-1961:1
na
1969:4-1970:4
1969:3-1970:1
1973:4-1975:1
1974:2-1975:1
1980:1-1980:3
1980:1-1980:3
1981:3-1982:4
1981:3-1982:1
1990:3-1991:1
1990:2-1991:1
2001:1-2001:4
na
2007:4-2009:2
2008:2-2009:2
4
Week 3 Answer Key
Econ 210D
K.D. Hoover
Spring 2015
Corrected, 4 February 2015
Problem 5.2:
(a) & (b)
Table 5.2.1: Characteristics of the U.S. Business Cycle
Shortest recession
Shortest boom
Shortest peak to peak
Shortest trough to trough
Longest recession
Longest boom
Longest peak to peak
Longest trough to trough
Median recession
Median boom
Median peak to peak
Median trough to trough
(a) After 1945
Date and duration
(in months)
January 1980 –July 1980
(6 months)
July 1980- July 1981
(12 months)
January 1980-July 1981
(18 months)
July 1980-November 1982
(28 months)
December 2007-June 2009
(18 months)
March 1991-March 2001
(120 months)
July 1990-March 2001
(128 months)
March 1991-November 2001
(128 months)
10 months
45 months
56 months
55 months
(b) Before 1942
Date and duration
(in months)
August 1918 – March 1919
(7 months)
March 1919 – January 1920
(10 months)
August 1918-January 1920
(17 months)
March 1919-July 1921
(28 months)
October 1873-March 1879
(65 months)
June 1938-Febuary 1945*
(80 months)
October 1873-March 1882
(101 months)
December 1870-March 1879
(99 months)
18 months
23 months
41 months
42.5 months
* If for the period strictly before 1942, the longest boom is March 1933-May 1937 (50 months)
(c) Some noticeably different characteristics before 1942 and after 1945 are as follows
1. The duration of the boom is longer after 1945: a) the median boom 45 months post-1945
versus 23 months pre-1942; b) the longest boom post-1945 is 120 months versus 50
months pre-1942.
2. The duration of the recession is shorter after 1945: a) the median slump post-1945 is 10
months versus 18 months pre-1942; the longest recession post-1945 is 18 months versus
pre-1945 65 months.
3. The duration of the complete cycle seems to be more than a year longer after 1945:
compare the complete cycles: peak-to-peak (56 months post-1945 versus 41 months pre1942) or trough to trough (55 versus 42.5 months).
5
Week 3 Answer Key
Econ 210D
K.D. Hoover
Spring 2015
Corrected, 4 February 2015
*Problem 5.3:
Table 5.3.1. Characteristics of U.S. Business Cycles: 1947-present
(percentage change in real GDP)
Mean
Median
Recession series
-1.8
Expansion series
24.9
Trough to trough
22.7
series
Peak to peak series
23.0
Note: Table 3 is based on Tables 5.3.2 and 5.3.3 below.
-2.2
20.6
16.8
19.0
Table 5.3.2.
Percentage Change in Real GDP in Recessions and Expansions: 1947- Present
Recession
1948:4-1949:4
1953:2-1954:2
1957:3-1958:2
1960:2-1961:1
1969:4-1970:4
1973:4-1975:1
1980:1-1980:3
1981:3-1982:4
1990:3-1991:1
2001:1-2001:4
2007:4-2009:2
Mean
Median
Percentage
change
–1.5
–2.4
–3.0
–0.3
–0.2
–3.1
–2.2
–2.5
–1.3
+0.5
–4.2
–1.8
–2.2
Expansion
1949:4-1953:2
1954:2-1957:3
1958:2-1960:2
1961:1-1969:4
1970:4-1973:4
1975:1-1980:1
1980:3-1981:3
1982:4-1990:3
1991:1-2001:1
2001:4-2007:4
Percentage
change
29.4
13.6
11.5
52.0
16.0
23.3
4.4
38.4
42.6
18.0
24.9
20.6
6
Week 3 Answer Key
Econ 210D
K.D. Hoover
Spring 2015
Corrected, 4 February 2015
Table 5.3.3.
Percentage Change in Real GDP in Complete Cycles: 1947- Present
Trough to
trough
1949:4-1954:2
1954:2-1958:2
1958:2-1961:1
1961:1-1970:4
1970:4-1975:1
1975:1-1980:3
1980:3-1982:4
1982:4-1991:1
1991:1-2001:4
2001:4-2009:2
Mean
Median
Percentage
change
26.2
10.3
11.2
51.8
12.4
20.6
1.7
36.5
43.3
13.0
22.7
16.8
Peak to peak
1948:4-1953:2
1953:3-1957:3
1957:3-1960:2
1960:2-1969:4
1969:4-1973:4
1973:4-1980:1
1980:1-1981:3
1981:3-1990:3
1990:3-2001:1
2001:1-2007:4
Percentage
change
27.4
11.5
8.2
51.6
15.8
19.5
2.1
34.8
40.7
18.6
23.0
19.0
Problem 5.4:
Table 5.4.1. Characteristics of U.S. Business Cycles: 1947-present
(change in the unemployment rate – percentage points)
Mean
Recession series
2.8
Expansion series
–2.5
Trough to trough series
0.2
Peak to peak series
0.1
Note: Table 6 is based on Tables 5.4.2 and 5.4.3 below.
7
Median
3.3
–2.3
–0.7
0.8
Week 3 Answer Key
Econ 210D
K.D. Hoover
Spring 2015
Corrected, 4 February 2015
Table 5.4.2.
Change in the Unemployment Rate in Recessions and Expansions: 1947- Present
Change
Change
Recession
1948:11-1949:10
1953:07-1954:05
1957:08-1958:04
1960:04-1961:02
1969:12-1970:11
1973:11-1975:03
1980:01-1980:07
1981:07-1982:11
1990:07-1991:03
2001:03-2001:11
2007:12-2009:06
Mean
Median
(percentage
points)
Expansion
1949:10-1953:07
1954:05-1957:08
1958:04-1960:04
1961:02-1969:12
1970:11-1973:11
1975:03-1980:01
1980:07-1981:07
1982:11-1990:07
1991:03-2001:03
2001:11-2007:12
4.1
3.3
3.3
1.7
2.4
3.8
1.5
3.6
1.3
1.2
4.5
2.8
3.3
(percentage
points)
–5.3
–1.8
–2.2
–3.4
–1.1
–2.3
–0.6
–5.3
–2.5
–0.5
–2.5
–2.3
Table 5.4.3.
Change in the Unemployment Rate in Complete Cycles: 1947- Present
Change
Change
Trough to trough
1949:10-1954:05
1954:05-1958:04
1958:04-1961:02
1961:02-1970:11
1970:11-1975:03
1975:03-1980:07
1980:07-1982:11
1982:11-1991:03
1991:03-2001:11
2001:11-2009:06
Mean
Median
(percentage
points)
Peak to peak
1948:11-1953:07
1953:07-1957:08
1957:08-1960:04
1960:04-1969:12
1969:12-1973:11
1973:11-1980:01
1980:01-1981:07
1981:07-1990:07
1990:07-2001:03
2001:03-2007:12
–2.0
1.5
–0.5
–1.0
2.7
–0.8
3.0
–4.0
–1.3
4.0
0.2
–0.7
(percentage
points)
–1.2
1.5
1.1
–1.7
1.3
1.5
0.9
–1.7
–1.2
0.7
0.1
0.8
Problem 5.5: For the “typical” post-World War II business cycle, on average, real GDP falls
about 1.8 percent during the recession while it increases 24.9 percent during the expansion.
The unemployment rate rises, on average, 2.8 percent during the recession while it falls 2.5
percent during the expansion. Changes in unemployment rates are highly variable across
8
Week 3 Answer Key
Econ 210D
K.D. Hoover
Spring 2015
Corrected, 4 February 2015
different cycles, but the mean values show that the gains in booms more or less offset losses
in recessions. Unemployment rates, of course, tend to move in the opposite direction to real
GDP.
The typical recession during post-World War II lasts about 10 months (as measured by the
median recession) while the expansion lasts about 45 months. Far from being symmetrical,
business cycles are four steps forward and one step back. Gains to GDP in expansions exceed
losses in recessions by more than 13 times. In the U.S., trend growth overwhelms cyclical
fluctuations.
For a complete cycle, the real GDP increases, on average about 23 percent. The complete
cycle lasts about 56 months about 4½ years (as measured by the median peak-to-peak
complete cycle – median trough-to-trough is similar). The business cycle seems to be
becoming stretched out over time: the last three complete cycles are include the first, third,
and fourth longest recorded.
Problem 5.6: There are four hypothesis indicated in the question:
A. big expansions are followed by big recessions (and small by small): correlation #1 should
be positive.
B. big recessions are followed by big expansions (and small by small): correlation #2 should
be positive.
C. small recessions are followed by big recoveries (and big by small). correlation #2 should
be negative.
D. expansions and recessions are essentially uncorrelated: both correlations should be small.
The evidence:
correlation #1 (expansion and the subsequent recession) = –0.61
correlation #2 (recession and the subsequent expansion) = –0.24
Hypothesis A and B are both ruled out, since both correlations are negative. Hypothesis D
depends on whether the two correlations are small (in absolute value) to count as zero, and
that depends on the size of the sample and statistical tests that are beyond this book; but it is
fair to say that correlation #1 is not small and correlation #2 is middling (perhaps small
enough to be zero, perhaps not). But in any case, Hypothesis D is not supported.
Another hypothesis, not suggested in the question, is
E. big expansions are followed by small recessions (and small by big): correlation #1 should
be negative.
Thus both Hypotheses C and D are supported. The two hypotheses suggest some patterns.
On the one hand, we could have a virtuous circle: large expansion  small recession 
large expansion  small recession  large expansion. But we could also have a vicious
9
Week 3 Answer Key
Econ 210D
K.D. Hoover
Spring 2015
Corrected, 4 February 2015
circle: large recession  small expansion  large recession  small expansion  large
recession. Because the correlations are not perfect, we should expect these chains to break
down from time to time, and breaking down could mean switching from a virtuous circle to a
vicious one or vice versa. Recent history has supported the circular pattern. The large
expansion of the mid- to late-1980s was followed by a weak recession in the early 1990s,
followed by the strong expansion of the later 1990s, followed by the very weak recession of
the early 2000s, followed by the relatively strong expansion of the early 2000. This looks like
a virtuous circle. But then the Great Recession of 2007-09 occurred. The recovery since then
has been relatively weak, suggesting that we may have slipped from a virtuous to a vicious
circle.
10